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Homework Help: Trying to solve the Poschl-Teller potential

  1. Dec 29, 2011 #1
    Trying to solve the Poschl-Teller potential (quantum mechanics)

    1. The problem statement, all variables and given/known data
    I have a superpotential that give me 2 of the Poschl-Teller potentials.
    The superpotential is:
    W(x)=-b*cot(x)
    The Poschl-Teller potentials are:
    J(x,b)=b(b-1)/(sin(x))^2-b^2
    K(x,b)=b(b+1)/(sin(x))^2-b^2
    2. Relevant equations
    Schrodinger equation: Hψ=Eψ
    3. The attempt at a solution
    I placed the potential in Schrodinger equation (neglecting the existence of constants) and received the following equations:
    ψ''(x)+(2E-J)ψ(x)=0
    ψ''(x)+(2E-K)ψ(x)=0
    I do not know what the next step I should do
    I know I need to get to Legendre polynomial but I don't know how...
    Can anyone show me how to do it?
     
  2. jcsd
  3. Dec 29, 2011 #2
    Put [itex]u=\cos x [/itex]. Rewrite the DE in the u variable....
     
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